Читать книгу Applied Univariate, Bivariate, and Multivariate Statistics - Daniel J. Denis - Страница 67

We have said that in a blocking design, between treatment conditions we expect the covariance to be unequal to 0. Now, consider a design in which, once again we block, but this time on more than two treatment levels. The layout for such a design is given in Table 2.9.

Now, here is the trick to understanding advanced modeling, including a primary feature of mixed effects modeling. We know that we expect the covariance between treatments to be unequal to 0. This is analogous to what we expected in the simple matched-pairs design. It seems then that a reasonable assumption to make for the data in Table 2.9 is that the covariances between treatments are equal, or at minimum, follow some hypothesized correlational structure. In multilevel and hierarchical models, attempts are made to account for the correlation between treatment levels instead of assuming these correlations to equal 0 as is the case for classical between‐subjects designs. In Chapter 6, we elaborate on these ideas when we discuss randomized block and repeated measures models.